JP2014190800A - Three-dimensional measuring method and three-dimensional measuring system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a three-dimensional measuring method and a three-dimensional measuring system for measuring a three-dimensional shape of a target by measuring the distance to the target capable of easily performing geometric calibration processing.SOLUTION: The three-dimensional measuring method includes the steps of: measuring a distance to a group of a flat surface 12 at a position of which is given as a flat surface equation 72 (step 33); calculating an estimation distance 55 to the flat surface based on a calibration parameter 80 and the flat surface equation 72 (step 51); and updating the calibration parameter 80 based on a piece of difference information 56 between a measured distance 62 and the estimation distance 55 (step 52b).

Description

  The present invention relates to a three-dimensional measurement method and a three-dimensional measurement apparatus that measure a three-dimensional shape of a measurement target by measuring a distance to the measurement target.

  There is a method of measuring the distance from an observation point (hereinafter referred to as “measurement reference point”) to the measurement target on the energy transmission path by observing the energy from the measurement target. For example, in the Time of Flight method, a light pulse or a sound wave pulse is applied to a measurement object, and the time until the light returns after being reflected is obtained. Also, in the focusing methods such as confocal method, Shape from Focus method, Shape from Defocus method, etc., the distance to the measurement object is changed in the optical axis direction, and the distance is obtained by searching the focal point of the image of the measurement object. . Furthermore, a measurement method capable of observing a tomographic image, such as OCT (Optical Coherence Tomography) of Patent Document 1, corresponds to measuring the distance to the boundary surface within the fault.

  The energy transmission path is a line segment starting from the measurement reference point (hereinafter referred to as “measurement line segment”). If this line segment formula is known, the measured distance is converted into a three-dimensional coordinate value. be able to. If such a distance measurement between two points is performed two-dimensionally over the entire measurement object, a three-dimensional point group representing the shape of the measurement object can be obtained.

  The measurement line segment dynamically changes due to environmental changes such as temperature, aging, and the like. Therefore, in order to guarantee the accuracy of the three-dimensional measurement, it is necessary to periodically perform “calibration” for updating the measurement line segment formula.

  A conventional three-dimensional measurement method and its calibration method will be described with reference to FIG.

  The three-dimensional measurement method 10 a has a function of measuring the distance (measurement distance 62) to the tooth 11 to be measured on the measurement line segment 81 starting from the measurement reference point 83 and extending in the direction vector 84. The three-dimensional measurement method 10 a converts the measurement distance 62 into the three-dimensional measurement coordinates 64 of the measurement point 63 using the measurement line segment formula of (Expression 1) and the distance conversion ratio 82 of the measurement distance.

ここで変換比率８２とは、計測距離から３次元座標系１４ａにおける距離への変換比率を表し、例えば、Time of Flight法では照射したエネルギーが帰ってくるまでの時間を計測するが、この時間を距離に変換する比率に相当する。

Here, the conversion ratio 82 represents the conversion ratio from the measurement distance to the distance in the three-dimensional coordinate system 14a. For example, in the Time of Flight method, the time until the irradiated energy returns is measured. Corresponds to the ratio converted to distance.

  A large number of measurement reference points 83 are distributed in a two-dimensionally broadened area (hereinafter referred to as a reference curved surface 290) (I × J in FIG. 2), and measured by the corresponding measurement line group 3 When the dimensional coordinates are collected, a three-dimensional point group 13 representing the three-dimensional shape of the measurement object 11 is obtained.

  The three-dimensional measurement method 10a includes a measurement process 20 that measures the three-dimensional coordinate 13 of the measurement object 11, a calibration process 50a that updates the calibration parameter 80, and data acquisition that acquires measurement data 60a that is an input to the calibration process 50a. It consists of process 30a.

  In the measurement process 20, first, in a distance measurement step 21, the distance to the measurement object 11 (measurement distance 23) is measured. Next, in the three-dimensional coordinate calculation step 22, the measurement distance 23 is converted into the corresponding three-dimensional coordinate 13 using the calibration parameter 80 as shown in (Expression 2).

３次元計測方法１０ａの校正では、撮像素子からなる平面１２ａを測定対象とし、まずデータ取得処理３０ａにより計測データ６０ａを取得し、次に校正処理５０ａが計測データ６０ａに基づいて校正パラメータ８０を更新する。

In the calibration of the three-dimensional measurement method 10a, the measurement target is the plane 12a made of an image sensor, first the measurement data 60a is acquired by the data acquisition process 30a, and then the calibration process 50a updates the calibration parameter 80 based on the measurement data 60a. To do.

  In the data acquisition process 30a, first, the plane 12a is moved in the Z direction using the Z stage 15a (step 31a). Next, the three-dimensional coordinate (measurement coordinate 64 of the measurement point) of the intersection of the plane 12a and the measurement line segment 81 is determined based on the pixel position of the image sensor and the stage position of the Z stage 15a (step 32a). And the measurement distance 62 to the plane 12a is measured (step 33). Steps 31a to 33 are repeated to obtain measurement data 60a for a plurality of measurement points 63.

  The calibration process 50a identifies the distance conversion ratio 82 by (Equation 3) using the measurement coordinates 64 and the measurement distances 62 of a plurality of measurement points (step 51a).

次に、同定した距離変換比率８２、計測座標６４および計測距離６２を用いて、（式４）により計測線分式８１の方向ベクトル８４と測定基準点８３を同定する（ステップ５２ａ）。

Next, using the identified distance conversion ratio 82, measurement coordinates 64, and measurement distance 62, the direction vector 84 and the measurement reference point 83 of the measurement line segment expression 81 are identified by (Expression 4) (Step 52a).

このような従来の技術としては、例えば特許文献２または非特許文献１に記載されたものが知られている。

As such conventional techniques, for example, those described in Patent Document 2 or Non-Patent Document 1 are known.

JP 2011-179902 A JP-A-1-214706 (FIG. 1)

Alkhazur M. et al: ”A Mathematical Model and Calibration Procedure for Galvanometric Laser Scanning Systems”, Vision, Modeling, and Visualization (2011) Z. Zhang, “A flexible new technique for camera calibration,” Technical Report MSRTR-98-71, Microsoft Research, Dec 1998. C. Ricolfe-Viala et al, "Improved Camera Calibration Method Based on a Two-Dimensional Template", Lecture Notes in Computer Science Volume 4478, 2007, pp 420-427 Kenichi Kanaya “Shape CAD and Mathematics of Figures” Kyoritsu Shuppan, 1998, p. 34

  However, in the conventional three-dimensional measurement method 10a, the accuracy of the calibration parameter 80 identified by the calibration process 50a is directly related to the measurement accuracy of the three-dimensional measurement coordinate 64 of the measurement point 63 according to (Equation 3) and (Equation 4). Dependent. Therefore, in order to realize high calibration accuracy, it is necessary to move the imaging element 12a having a high resolution by the Z stage 15a that can accurately position the imaging element 12a. Therefore, the conventional calibration method is suitable for an apparatus having an originally movable stage such as a confocal laser microscope.

  However, since a 3D hand scanner such as an intraoral 3D scanner (ODS: Oral Direct Scanner) does not require a movable stage during normal operation, it is necessary to provide a separate stage for calibration using the conventional method. The device configuration is complicated. In addition, since the conventional method requires accurate positioning of the Z stage, an automatic movement mechanism is provided on the Z stage or moved by a user operation, which complicates the apparatus configuration or complicates the user operation. . That is, the conventional three-dimensional measurement method and three-dimensional measurement apparatus have a problem that the configuration for calibration and the user operation are complicated.

  The present invention solves the above-described conventional problems, and an object thereof is to provide a three-dimensional measurement method and a three-dimensional measurement apparatus capable of executing calibration with a simple configuration / operation.

  In order to solve the above-described conventional problems, the three-dimensional measurement method of the present invention includes a step of measuring a distance to a measurement target on a measurement line segment starting from a measurement reference point, and the predetermined three-dimensional coordinate system. A three-dimensional measurement method including a step of calculating a three-dimensional coordinate of a measurement object from the distance using a line segment expression representing a measurement line segment and a conversion ratio of a measurement distance in the three-dimensional coordinate system, A first step of measuring a first distance on the measurement line segment to a plurality of planes expressed as a plane equation, and using the plane equation, the line segment formula, and the conversion ratio, A second step of calculating an estimated value for the first distance; a third step of updating the line segment formula and the conversion ratio based on difference information between the first distance and the estimated value; Update the line segment formula and the conversion ratio A fourth step for determining whether or not to end, and repeating the second step, the third step, and the fourth step until it is determined in the fourth step to end It is.

  In addition, the three-dimensional measurement apparatus of the present invention includes a measurement unit that measures a distance to a measurement target on a measurement line segment starting from a measurement reference point, and a line segment that represents the measurement line segment in a predetermined three-dimensional coordinate system. A three-dimensional measurement apparatus having a coordinate calculation unit that calculates a three-dimensional coordinate of a measurement target from the distance using an equation and a conversion ratio of a measurement distance in the three-dimensional coordinate system, where the position is expressed as a plane equation In addition, a plane distance measuring unit that measures a first distance on the measurement line segment to a plurality of planes, and the plane equation, the line segment formula, and the conversion ratio are used for the first distance. A distance estimating unit that calculates an estimated value; a parameter updating unit that updates the line segment formula and the conversion ratio based on difference information between the first distance and the estimated value; and the line segment formula and the conversion ratio. End of calibration to determine whether renewal should end Has a tough, said distance estimation unit until it is determined to be terminated in the calibration end determining unit, in which is characterized by repeating the processing in the parameter updating unit and the calibrating end determining unit.

  In the three-dimensional measurement method according to the present invention, the positional information necessary for calibration is only the plane equation of the measurement target plane, and therefore the measurement step for calibration can be simplified as compared with the conventional calibration method based on the three-dimensional coordinates of the measurement point. .

  In the three-dimensional measuring apparatus according to the invention, since the position information necessary for calibration is only the plane equation of the measurement target plane, a mechanism for calibration is provided rather than a conventional apparatus that implements calibration based on the three-dimensional coordinates of the measurement point. It can be simplified.

Process flow diagram of three-dimensional measurement method in Embodiment 2 of the present invention Process flow diagram and schematic diagram of 3D measurement method according to the prior art The figure explaining one effect of this invention Schematic diagram of an apparatus according to Embodiment 1 of the present invention Configuration diagram of an apparatus according to Embodiment 1 of the present invention Overview diagram of measurement processing in Embodiment 1 of the present invention Processing flow diagram in Embodiment 1 of the present invention Overview of plane identification processing in Embodiment 1 of the present invention Processing outline diagram of calibration parameter identification in Embodiment 1 of the present invention Configuration diagram of apparatus in embodiment 2 of the present invention

  Embodiments of a three-dimensional measurement method and a three-dimensional measurement apparatus according to the present invention will be described below in detail with reference to the drawings.

(Embodiment 1)
FIG. 4 shows an outline of an OCT-ODS (Oral Direct Scanner) apparatus according to the first embodiment of the present invention.

  The OCT-ODS apparatus 100 is an apparatus for measuring a three-dimensional shape of the tooth 11 by an operator such as a dentist (hereinafter referred to as a user) inserting the probe 230 into a patient's oral cavity by hand. The measurement is executed by positioning the measurement head 235 at the tip of the probe 230 on the measurement target portion of the tooth 11 and pressing the measurement switch 239. The measurement result is processed by the main body 101 and output as a group of three-dimensional coordinates 13 on the display unit 304.

  The configuration of the OCT-ODS apparatus 100 will be described based on FIG.

  The OCT-ODS apparatus 100 includes a distance measurement unit 200, a coordinate measurement unit 300, a plane identification unit 400, and a calibration processing unit 500, a measurement data memory 1 (130), a measurement data memory 2 (131), and a plane. There are four memories, an information memory 140 and a calibration parameter memory 150. The operation of each functional block and its components is controlled by the control unit 110 via the control bus 120.

  The distance measurement unit 200 measures the measurement distance group to the measurement target tooth 11 by irradiating the measurement target tooth 11 with the beam-shaped measurement light 17 using the measurement switch 239 as a trigger and observing the return light. The measurement light 17 is generated by dividing the light beam emitted from the wavelength swept light source 210 into the measurement light 17 and the reference light 18 by the beam splitter 220, and irradiates the tooth 11 to be measured via the probe 230. The return light from the tooth 11 to be measured reaches the interference unit 250 via the probe 230, and interferes with the reference light 18 that passes through the reference mirror 240, thereby generating interference light 19. The intensity of the interference light 19 is detected by the light receiving unit 260, and the detection result is subjected to data processing by the signal processing unit 270 and the interface detection 280, thereby measuring the distance to the tooth 11 to be measured. Details of this data processing will be described later.

  Since the measurement light 17 is two-dimensionally scanned by the optical scanning unit 231 in the probe, the distance measurement is performed over the entire surface area of the tooth 11 to be measured.

  At the same time as the distance measurement, the distance measurement unit 200 observes the visible light 48 from the measurement target tooth 11 with the camera unit 237 in the probe, and also generates a two-dimensional image of the measurement target.

  The OCT-ODS apparatus 100 executes the measurement process of the tooth 11 to be measured when the measurement head 235 is provided at the tip of the probe 230, but if the calibration head 236 is provided, the OCT-ODS apparatus 100 is geometric. Perform calibration processing. In this mode switching between the measurement mode and the calibration mode, the type of the head equipped with the head sensor 238 is detected and notified to the control unit 110, and in response to this, the control unit 110 changes to the current head type. Based on this, the destination of the output from the distance measurement unit 200 (measurement distance group and measurement target two-dimensional image) is switched by the data flow changeover switches 160 and 170.

  In the measurement mode, as shown in FIG. 5, the measurement distance group from the distance measurement unit 200 and the two-dimensional image to be measured are both passed to the coordinate measurement unit 300. The measured group of measured distances 23 is converted into a group of three-dimensional coordinates 13 by the three-dimensional coordinate calculation 301 based on the distance conversion ratio 82 and the measurement line segment 81 in the calibration parameter memory. The group is drawn on the display unit 304 by the point cloud drawing 302. The input two-dimensional image to be measured is displayed on the display unit 304 by the preview screen drawing 303.

  In the calibration mode, the output from the distance measuring unit 200 is stored in the memory. That is, the measurement distance group is stored in the measurement data memory 2 (131), and the two-dimensional image to be measured is stored in the measurement data memory 1 (130).

  The measurement target in the calibration mode is the plane 12 attached to the calibration head 236. Since the plane 12 is inclined and attached via a spiral groove (hereinafter referred to as the plane moving unit 15) of the calibration head 236, the distance and the inclination with respect to the calibration head 236 can be obtained by turning the plane 12. Can be changed. Therefore, when the user appropriately turns the chart of the plane 12 and presses the measurement switch 239, the group of the two-dimensional image 61 and the measurement distance 62 with respect to the plane 12 at different positions becomes the measurement data memory 1 (130) and the measurement. The data is stored in the data memory 2 (131).

  Thereafter, when the calibration head 236 is removed and the measurement head 235 is attached, the control unit 110 activates the plane identification unit 400 and the calibration processing unit 500. The plane identification unit 400 identifies a group of plane equations 72 representing the position of the plane 12 based on the group of plane two-dimensional images 61 in the measurement data memory 1 (130), and passes the group to the calibration processing unit 500. The calibration processing unit 500 calculates the distance conversion ratio 82 and the measurement line segment 81 in the calibration parameter memory 150 based on the group of the plane equation 72 and the group of the measurement distance 62 in the measurement data memory 2 (131). Update.

  Details of the data flow in the calibration mode will be described with reference to FIG.

  In order to specify the three-dimensional coordinate 13, it is necessary to introduce a three-dimensional coordinate system. Here, the camera coordinate system of the camera unit 237 is a three-dimensional coordinate system 14.

  The wavelength swept light source 210 temporally changes the emission frequency of the emitted beam light. The light emission frequency of the beam light periodically changes in a sawtooth shape as shown in FIG. 6, and this one period (referred to as A scan period) corresponds to the measurement time in one measurement line segment 81.

  The beam light emitted from the wavelength swept light source 210 is divided into the measurement light 17 and the reference light by the beam splitter 220. The measurement light 17 is incident on the plane 12 via the optical scanning unit 231, diffusely reflected, and returns to the interference unit 250 along the reverse path. The reference light 18 is reflected by the reference mirror and reaches the interference unit 250.

  The optical scanning unit 231 has two scanning mirrors (B scan mirrors) that scan in two primary directions (B scan direction 291 and C scan direction 292) in order to two-dimensionally scan the irradiation destination of the measurement light 17. 232, C scan mirror 233). The direction of the measuring light swung by the scanning mirror is adjusted by the lens 234. The B scan mirror 232 creates J scan points in the B scan direction 291. At least the A-scan period remains at each scanning point. The C scan mirror 233 creates I scan points in the C scan direction 292, but remains at each scan point until the scanning for one line in the B scan direction 291 is completed. Thereby, I × J scanning points can be evenly distributed on a two-dimensional surface (for example, the reference curved surface 290).

  The interference unit 250 interferes with the measurement light 17 and the reference light 18 to generate interference light 19, and the light receiving unit 260 measures the intensity thereof. The interference light intensity is Fourier transformed by the signal processing unit 270 to generate a tomographic image 600.

  The tomographic image 600 is a two-dimensional scalar field representing the distribution of interference light intensity in a space having the B scan direction as the horizontal axis and the interference light frequency as the vertical axis. As described in Patent Document 1, the interference light frequency has a linear relationship with the optical path length difference between the measurement light 17 and the reference light 18.

  Therefore, if a point on the optical path of the measurement light 17 equal to the optical path length of the reference light 18 is defined as a measurement reference point 83, the plane 12 from the measurement reference point 83 in the light beam direction of the measurement light 17 (hereinafter referred to as a direction vector 84). Is a linear relationship with the vertical axis of the tomographic image 600 (that is, the interference light frequency). This linear coefficient is the distance conversion ratio 82, and the interference light frequency is the measurement distance 62.

  In the tomographic image 600, the intensity becomes maximum at the interference light frequency corresponding to the surface of the plane 12, and the intensity decreases as the distance to the inside of the plane decreases due to scattering / absorption. Therefore, in the interface detection 280, the interference light frequency corresponding to the intensity peak position in the tomographic image 600 is set as the measurement distance 62 to the surface of the plane 12. The value obtained by multiplying the measurement distance 62 by the distance conversion ratio 82 (corrected measurement distance) is the distance to the plane 12 on the line segment (measurement line segment 81) in the direction vector 84 starting from the measurement reference point 83. Equivalent to.

The measurement line segment 81 and the distance conversion ratio 82 are stored in the calibration parameter memory 150 as geometric calibration parameters.
Since there are I × J measurement line segments 81 by the optical scanning unit 231 as described above, I × J measurement distance groups can be obtained by one measurement. Therefore, this measurement is performed by measuring the distance between the curved surface (reference curved surface 290) composed of I × J measurement reference points 83 and the plane 12 at I × J sampling points (that is, measurement reference points 83). Is equivalent to When this distance measurement between the reference curved surface 290 and the plane 12 is repeated K times by moving the plane 12 to a different position using the plane moving unit 15, a group of I × J × K measurement distances 62 is obtained. This is stored in the measurement data memory 2 (131).

  Simultaneously with the acquisition of the group of the measurement distance 62, the camera unit 237 takes a two-dimensional image of the plane 12 at each position and stores it in the measurement data memory 1 (130). The projection operation from the 3D to the 2D in the camera unit 237 is described by the camera parameter 71, and the camera parameter 71 is also stored in the plane information memory 140.

  The plane identification unit 400 and the calibration processing unit 500 are activated by the control unit 110 that detects that the probe tip is replaced from the calibration head 236 to the measurement head 235.

The plane identification unit 400 identifies a plane equation 72 representing each position on the plane 12. This identification is
This is realized by updating the group of plane equations 72 stored in the plane information memory 140. That is, the plane identification unit 400 receives a group of plane two-dimensional images 61 in the measurement data memory 1 (130), the camera parameters 71 and the plane equation 72 in the plane information memory 140, and outputs an updated plane equation 72. This is stored in the plane information memory 140. Details of the plane identification processing algorithm will be described later.

  The calibration processing unit 500 is activated when the update of the group of plane equations 72 by the plane identification unit 400 is completed. The calibration processing unit 500 receives as input the group of measurement distances 62 in the measurement data memory 2 (131), the group of plane equations 72 in the plane information memory 140, the distance conversion ratio 82 and the measurement line segment 81 in the calibration parameter memory. The updated plane equation group 72, the updated distance conversion ratio 82, and the updated measurement line segment 81 are output. If the calibration processing unit 500 determines that the identification of the group of the plane equation 72 has not yet converged, the calibration processing unit 500 activates the plane identification unit 400 again. Details of the calibration processing algorithm will be described later.

  A three-dimensional measurement method 10 mounted on the OCT-ODS apparatus 100 will be described with reference to FIG.

  The three-dimensional measurement method 10 includes a measurement process 20 executed in the measurement mode, a data acquisition process 30, a plane identification process 40, and a calibration process 50 executed in the calibration mode. The data to be processed by the three-dimensional measurement method 10 includes a measurement distance 23 to be measured, measurement data 60, plane information 70, and calibration parameters 80, each of which is a measurement data memory 1 of the OCT-ODS apparatus 100. (130), measurement data memory 2 (131), plane information memory 140, and calibration parameter memory 150.

  The measurement process 20 has been described with reference to FIG. Therefore, only correspondence with the OCT-ODS apparatus will be described here. The measurement distance 23 generated in the distance measurement step 21 corresponds to a group of measurement distances 62 generated by the interface detection 280 of the OCT-ODS apparatus 100 (see FIGS. 5 and 6). The three-dimensional coordinate calculation step 22 corresponds to the three-dimensional coordinate calculation 301 of the OCT-ODS apparatus 100 (see FIG. 5).

  When the calibration mode is entered, a data acquisition process 30 is executed.

  In the data acquisition process 30, the plane is first moved (step 31). In the OCT-ODS apparatus 100, the user moves the plane 12 by turning (see FIG. 5).

  In the data acquisition process 30, next, a two-dimensional image of feature points on the plane is generated (step 32). As shown in FIG. 6, the OCT-ODS apparatus 100 has a circle mark on the plane 12, and this center is a feature point 46. Taking a two-dimensional image 61 of a plane with the camera unit 237 and obtaining the center coordinates of a circle mark in the two-dimensional image 61 corresponds to generating the two-dimensional image 61 of feature points.

  In the data acquisition process 30, the distance to the plane is next measured (step 33). In the OCT-ODS apparatus, as described with reference to FIG. 6, the distance measurement between the reference curved surface 290 and the plane 12 output by the interface detection 280 corresponds to the output of this step.

  In the data acquisition process 30, Steps 31 to 33 are performed as many times as necessary (K times in this embodiment), and measurement data 60 at a plurality of different positions on the plane 12 is acquired. K is at least 7 or more in order to identify the calibration parameter 80 having seven unknown variables, and is preferably 20 or more in consideration of measurement errors.

  When the necessary number of measurement data 60 has been acquired, the user replaces the probe tip from the calibration head 236 to the measurement head 235, and the execution of the plane identification processing 40 is triggered by this. The plane identification process 40 is implemented by the plane identification unit 400 of the OCT-ODS apparatus 100.

  The plane identification process 40 first generates an estimated image 44 of feature points on the plane based on the camera parameter 71 and the plane equation 72 as input (step 41). Next, the camera parameter 71 and the plane equation 72 are updated based on the difference information 45 between the two-dimensional image 61 of the feature points and the estimated image 44 (step 42). Finally, based on the camera parameters 71 and the convergence state of the plane equation 72, etc., it is determined whether or not the plane identification process should be terminated. If it should not end, step 41 is executed again. If it should end, execution of the calibration process 50 is started.

  Details of the plane identification process will be described with reference to FIG.

  FIG. 8 shows an image projected onto the image plane 47 by the camera unit 237 while moving the plane 12 to a plurality of positions (first plane position,..., Kth plane position,...). Represents the state of being.

  For each plane position, an object coordinate system 16 is introduced in which the x-axis direction and y-axis direction of the two-dimensional coordinate system on the plane 12 are the x-axis and y-axis, and the normal vector direction of the plane 12 is the z-axis. . The three-dimensional coordinates for the same feature point 46 have the same value in the target coordinate system regardless of the plane position (that is, the two-dimensional coordinates of the feature point 46 are expanded to three dimensions with Z = 0). The coordinate transformation from the target coordinate system 16 to the three-dimensional coordinate system 14 is described by a rotation matrix 77 and a translation vector 78. Therefore, if the two-dimensional coordinates of the feature points on the plane are all known, the coordinates in all the three-dimensional coordinate systems 14 are determined only by the rotation matrix 77 and the translation vector 78, regardless of the number of feature points.

  Projection by the camera unit 237 is modeled by camera parameters 71. As shown in (Equation 5), the internal parameter matrix 73 representing the central projection, the distortion coefficient vector 74 describing the lens distortion, the rotation matrix 77 and the translation vector 78 are used as parameters, and the feature point 46 is projected onto the image plane 47. In this case, the estimated image 44 can be calculated.

前記のステップ４１（特徴点の推定画像を生成する）で（式５）による推定を実行する。（式５）の詳細は非特許文献２を参照のこと。

In step 41 (generate an estimated image of feature points), the estimation according to (Equation 5) is executed. See Non-Patent Document 2 for details of (Formula 5).

  If the parameters (camera parameter 71, rotation matrix 77, or translation vector 78) are not correct, the calculated estimated image 44 produces a difference 45 from the actually observed image 61. Accordingly, the norm sum of squares of the difference 45 is used as a cost function (Equation 6), and a parameter value that minimizes the function value is identified by a nonlinear optimization method.

同定された回転行列７７と並進ベクトル７８から、（式７）により平面方程式７２を求める。

From the identified rotation matrix 77 and translation vector 78, a plane equation 72 is obtained by (Expression 7).

このカメラパラメータと平面方程式の更新は前記のステップ４２で実行する。

The updating of the camera parameters and the plane equation is executed in step 42 described above.

  In FIG. 8, a method based on the camera parameter calibration method described in Non-Patent Document 2 is used as step 41 for generating the estimated image of the feature point. Yes, here is just an example.

  Returning to the description of FIG.

  When the plane identification process 40 is completed, the calibration process 50 is started. The calibration process 50 is implemented by the calibration processing unit 500 of the OCT-ODS apparatus 100.

  The calibration process 50 first generates an estimated value 55 of the distance to the plane based on the plane equation 72, the measurement line segment formula 81, and the measurement distance conversion ratio 83 (step 51). Next, the plane equation 72, the measurement line segment 81, and the measurement distance conversion ratio 83 are updated based on the difference information 56 between the measured value 62 and the estimated value 55 of the distance to the plane (step 52). Next, it is determined whether or not the calibration process should be terminated based on the convergence state of the plane equation 72, the measurement line segment 81, and the measurement distance conversion ratio 83 (step 53). If not, the step 51 is executed again. If it should be terminated, it is determined whether or not the plane identification process should be re-executed based on the convergence state of the plane equation 72 and the like (step 54). If it should be re-executed, the plane identification process 40 is executed again. If it should not be re-executed, the calibration process is terminated.

  In FIG. 7, the plane equation 72 is also updated in step 52, and the result is fed back to the plane identification process 40 in step 54 to repeatedly execute the plane identification process 40 and the calibration process 50. These processes can be omitted if the accuracy of the above can be ensured. That is, in the calibration process 50, only the line segment formula 82 and the conversion ratio 82 are updated in step 52, and step 54 can be deleted.

  Details of the calibration processing 50 will be described with reference to FIG.

  FIG. 9 illustrates a situation in which the distance 62 on the measurement line segment 81 to the plane 12 at K positions is being measured.

  The distance to the plane 12 whose position is represented by the plane equation 72 can be calculated as an estimated value 55 by (Equation 8) as the distance to the intersection 66 of the measurement line segment formula 81 and the plane equation 72. See Non-Patent Document 4 for the derivation of (Equation 8).

前記のステップ５１（平面への距離の推定値５５を生成する）で（式８）による推定を実行する。

In step 51 (generating the estimated value 55 of the distance to the plane), the estimation according to (Equation 8) is executed.

  If the parameters (the plane equation 72, the measurement line segment expression 81, and the measurement distance conversion ratio 83) are not correct, the calculated estimated distance 55 produces a difference 56 from the actually measured distance 62. Therefore, the square sum of the differences 56 is used as a cost function (Equation 9), and a parameter value that minimizes the function value is identified by a nonlinear optimization method.

前記のステップ５２（平面方程式７２、計測線分８１および計測距離変換比率８３を更新する）で（式９）によるパラメータの更新を実行する。

In step 52 (the plane equation 72, the measurement line segment 81, and the measurement distance conversion ratio 83 are updated), the parameter is updated according to (Equation 9).

  Even if the distance to the plane 12 at the parallel position is measured, the constraint on the measurement line segment does not increase. For this reason, the parameter update in (Equation 9) fails when all K positions on the plane 12 are parallel. Therefore, in the first embodiment, as shown in FIG. 5, the flat surface 12 is attached to the calibration head 236 at an inclined angle, and this inclination angle is changed by rotation.

  As described above, in the first embodiment, since the positional information necessary for calibration is only the plane equation 72 of the plane 12, calibration is performed with a simpler mechanism than the conventional calibration method based on the three-dimensional coordinates 64 of the measurement point. it can. As shown in FIG. 3, the identification of the plane equation 72 is more accurate than the case where the coordinates 64 of one point 63 on the plane are identified. That is, even when there is a random error 65 in the measurement of one point, in the plane equation 72 identified by fitting a plurality of points, the random error at each point is canceled and the error 79 is reduced. For this reason, in the first embodiment, the mechanism for realizing the calibration is simplified as compared with the prior art without reducing the calibration accuracy. That is, the plane equation 72 can be identified only by photographing the two-dimensional image group 61 of the plane 12 having the feature point 46 on the surface by the camera unit 237 used for the preview screen drawing 303 during the normal measurement process 20. Yes, no additional calibration mechanism is required.

  In the first embodiment, the user equips the head of the probe 230 with the calibration head 236 and rotates the plane 12 attached thereto via the plane moving unit 150 (the rotation angle accuracy is obtained in this rotation). The measurement data 60 for calibration can be acquired by this, so that the user operation for calibration is simpler than the conventional method of setting the Z position of the Z stage 15a accurately. .

(Embodiment 2)
FIG. 10 shows a three-dimensional measuring apparatus according to the second embodiment of the present invention. In the first embodiment, the plane equation 72 is identified by the plane identification unit 400 in the three-dimensional measurement apparatus (OCT-ODS apparatus 100). However, in the second embodiment, the plane identification apparatus 400a provided outside the three-dimensional measurement apparatus 100a. Identifies. As the plane identification device 400a, a device added with a function of identifying a plane equation that fits from a three-dimensional point group measured by a calibrated three-dimensional measurement device, or the camera unit 237 of the first embodiment and a plane An apparatus having the identification unit 400 may be used.

  The plane identification device 400a observes the plane group 12 (may be a plurality of planes, or one plane may be moved to a different position as in the first embodiment), and the corresponding plane equation group 72 is output. The three-dimensional measurement apparatus 100a measures the measurement distance group 62 for the same plane group 12, and updates the calibration parameter 80 based on this and the plane equation group 72 from the plane identification apparatus 400a.

  FIG. 1 shows a three-dimensional measurement method 10 implemented by the three-dimensional measurement apparatus 100a.

  Differences from the first embodiment (FIG. 7) will be described.

  In the data acquisition process 30, the two-dimensional image 61 of the feature points acquired in the first embodiment is not necessary, and only the measurement distance group 62 with respect to the plane group 12 is acquired.

  Since the plane equation group 72 is given from the outside as an input, the plane identification process 40 of the first embodiment is not necessary.

  In step 52b of the calibration process 50, only the line segment formula 81 and the conversion ratio 82 are updated, and the plane equation 72 updated in step 52 of the first embodiment is not changed. Accordingly, step 54 of the first embodiment (determining whether the plane identification process should be re-executed) becomes unnecessary.

  Therefore, the three-dimensional measurement method 10 of the second embodiment is the following procedure.

  When the calibration process is activated, the distance 62 to the plane group on the measurement line segment is measured (step 33a), and the process proceeds to the execution of the calibration process 50.

  The calibration process 50 generates an estimated value 55 of the distance to the plane based on the measurement line segment formula 81, the measurement distance conversion ratio 82, and the given plane equation 72 (step 51). Next, the measurement line segment 81 and the measurement distance conversion ratio 83 are updated based on the difference information 56 between the measured value 62 and the estimated value 55 of the distance to the plane (step 52b). Finally, based on the convergence state of the measurement line segment 81 and the measurement distance conversion ratio 83, it is determined whether the calibration process should be terminated (step 53). If not, the step 51 is executed again. If it should be terminated, the calibration process is terminated.

  As described above, in the second embodiment, since the three-dimensional measurement apparatus 100a has only the plane equation 72 of the plane 12 as the positional information necessary for calibration, the conventional calibration method based on the three-dimensional coordinates 64 of the measurement points. Can be calibrated with a simple mechanism.

  In the second embodiment, the mechanism necessary for calibration is the plane identification device 400a. However, in the conventional example, a three-dimensional measurement device that measures the position of a point is required instead. As described above, since the point coordinate value 64 directly affects the calibration accuracy, the three-dimensional measurement device for measuring the point coordinate value needs higher measurement accuracy than the three-dimensional measurement device 100a to be calibrated.

  On the other hand, the plane identification device 400a that measures the position as the plane equation 72 as described with reference to FIG. 3 can identify the plane with higher accuracy than the measurement accuracy of individual point coordinates, and thus is simplified as the plane identification device 400a. It is possible to use a three-dimensional measuring apparatus. For example, an apparatus including only the camera unit 237 and the plane identification unit 400 described in the first embodiment may be used.

  The three-dimensional measurement method and the three-dimensional measurement apparatus according to the present invention are useful for application to a three-dimensional hand scanner, a small three-dimensional measurement apparatus, and the like because the mechanism for calibration and the user operation are simplified.

DESCRIPTION OF SYMBOLS 10 3D measuring method 10a 3D measuring method 11 Tooth 12 Plane 12a Image pick-up element 13 3D coordinate 14 3D coordinate system 14a 3D coordinate system in a prior art 15 Plane moving part 15a Z stage 16 Target coordinate system 17 Measurement light 18 reference Light 19 Interference light 20 Measurement processing 21 Distance measurement step 22 Three-dimensional coordinate calculation step 23 Measurement distance 30 Data acquisition processing 30a Data acquisition processing in the prior art 31 Step of moving the plane 31a Step of moving the plane in the Z direction 32 Plane by the camera Step of generating a two-dimensional image of the upper feature point 32a Step of identifying the three-dimensional coordinates of the measurement point from the pixel position and the Z stage position 33 Step of measuring the distance to the plane on the measurement line segment 33a Measurement line segment Measuring the distance to the plane group above 40 Surface identification process 41 Step of generating an estimated image of a feature point on a plane 42 Step of updating camera parameters and plane equations 43 Step of determining whether or not to end the plane identification process 44 Estimated image 45 Difference information 46 Feature point 47 Image plane 48 Visible light 50, 50a Calibration processing 51 Step for calculating an estimated value of the distance to the plane on the measurement line segment 51a Step for identifying the distance conversion ratio 52 Step for updating the line segment formula, conversion ratio, and plane equation 52a Measurement line Step 52b for recognizing a division formula Step 53 for updating a line segment formula and conversion ratio 53 Step for judging whether calibration processing should be terminated 54 Step for judging whether plane identification processing should be re-executed 55 Estimated distance 56 Difference information 60 Measurement data 60a Conventional Measurement data in technology 61 Two-dimensional image 62 Measurement distance 63 Fixed point 64 Three-dimensional measurement coordinates 65 Measurement error 66 Intersection of plane and measurement line segment 70 Plane information 71 Camera parameter 72 Plane equation 73 Internal parameter matrix 74 Distortion coefficient vector 75 Plane normal vector 76 Origin and plane distance 77 Rotation Matrix 78 Translation vector 79 Plane measurement error 80 Calibration parameter 81 Measurement line segment 82 Distance conversion ratio 83 Measurement reference point 84 Direction vector 100 OCT-ODS device 100a Three-dimensional measurement device 110 Control unit 120 Control bus 130 Measurement data memory 1
131 Measurement data memory 2
140 Plane information memory 150 Calibration parameter memory 160 Switch 170 Measurement distance output switch 200 Distance measurement unit 210 Wavelength sweep light source 220 Beam splitter 230 Probe 231 Optical scanning unit 232 B scan mirror 233 C scan mirror 234 Lens 235 Measuring head 236 For calibration Head 237 Camera unit 238 Head sensor 239 Measurement switch 240 Reference mirror 250 Interference unit 260 Light receiving unit 270 Signal processing unit 280 Interface detection 290 Reference curved surface 291 B scan direction 292 C scan direction 300 Coordinate measurement unit 301 Three-dimensional coordinate calculation 302 Point group drawing 303 Preview Screen Drawing 304 Display Unit 400 Plane Identification Unit 400a Plane Identification Device 500 Calibration Processing Unit 600 Tomographic Image

Claims (6)

Measuring the distance to the measurement object on the measurement line segment starting from the measurement reference point;
A step of calculating three-dimensional coordinates of a measurement target from the distance using a line segment expression representing the measurement line segment in a predetermined three-dimensional coordinate system and a conversion ratio of the measurement distance in the three-dimensional coordinate system. Measuring method,
A first step of measuring a first distance on the measurement line segment to a plurality of planes, the position of which is expressed as a plane equation;
A second step of calculating an estimate for the first distance using the plane equation, the line segment formula and the conversion ratio;
A third step of updating the line segment formula and the conversion ratio based on difference information between the first distance and the estimated value;
A fourth step of determining whether to update the line segment formula and the conversion ratio;
A three-dimensional measurement method in which the second step, the third step, and the fourth step are repeated until it is determined to end in the fourth step. The first step includes
A fifth step of moving the plane while changing its inclination;
A sixth step of generating a two-dimensional image of the feature points on the plane by a camera;
A seventh step of measuring the first distance;
An eighth step of generating an estimated image of the two-dimensional image based on the camera parameters of the camera and the plane equation;
From the ninth step of updating the camera parameter and the plane equation based on the difference information between the two-dimensional image and the estimated image, and the tenth step of determining whether the updating of the camera parameter and the plane equation should be finished. Become
The three-dimensional measurement method according to claim 1, wherein the eighth step, the ninth step, and the tenth step are repeated until it is determined in the tenth step that the process is ended. Updating the plane equation in the third step;
An eleventh step for determining whether to update the camera parameter and the plane equation again, which is executed when it is determined to end in the fourth step;
3. The three-dimensional measurement method according to claim 2, wherein when it is determined in the eleventh step that updating is necessary, the eighth step and subsequent steps are re-executed. A measurement unit that measures the distance to the measurement target on the measurement line segment starting from the measurement reference point;
Using a line segment expression representing the measurement line segment in a predetermined three-dimensional coordinate system and a conversion ratio of the measurement distance in the three-dimensional coordinate system, a coordinate calculation unit that calculates the three-dimensional coordinates of the measurement target from the distance A three-dimensional measuring device,
A plane distance measuring unit that measures a first distance on the measurement line segment to a plurality of planes, the positions of which are expressed as a plane equation;
A distance estimation unit that calculates an estimated value for the first distance using the plane equation, the line segment formula, and the conversion ratio;
A parameter updating unit that updates the line segment formula and the conversion ratio based on the difference information between the first distance and the estimated value;
A calibration end determination unit for determining whether to update the line segment formula and the conversion ratio;
A three-dimensional measurement apparatus that repeats the processing in the distance estimation unit, the parameter update unit, and the calibration end determination unit until the end of calibration is determined to be ended. The plane distance measuring unit is
A plane moving unit that moves the plane while changing its inclination;
An imaging unit for generating a two-dimensional image of the feature points on the plane by a camera;
A distance measuring unit for measuring the first distance;
An image estimation unit that generates an estimated image of the two-dimensional image based on the camera parameters of the camera and the plane equation;
From a plane update unit that updates the camera parameter and the plane equation based on difference information between the two-dimensional image and the estimated image, and a plane identification end determination unit that determines whether to update the camera parameter and the plane equation Become
The three-dimensional measurement apparatus according to claim 4, wherein the processes in the image estimation unit, the plane update unit, and the plane identification end determination unit are repeated until it is determined as end by the plane identification end determination unit. Update the plane equation in the parameter update unit,
A process is started when it is determined that the calibration end determination unit ends, and a plane re-identification determination unit that determines whether to update the camera parameter and the plane equation again,
The three-dimensional measurement apparatus according to claim 5, wherein when the surface re-identification determination unit determines that updating is necessary, the processing unit subsequent to the image estimation unit is re-executed.

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